SamplePublisher`GrassmannCalculus`
OrthonormalBasis  |
|
| | ||||
Details and Options
Examples
(1)
Basic Examples
(1)
In[1]:=
<<GrassmannCalculus`
Set a 2-dimensional Point space.
In[2]:=
 | SetCoordinateVectorSpace |
The various types of basis vectors are:
In[3]:=
 | OrthonormalBasis |
| VectorBasis |
| FormBasis |
Out[3]=
,
e
x
e
y
Out[3]=
{,}
e
x
e
y
Out[3]=
{dx,dy}
The active basis is currently the .
FormBasis
In[4]:=
{BasisType,Basis}
Out[4]=
{Form,{dx,dy}}
Since we have a Euclidean metric we can easily transition a Grassmann expression between the various bases types with the built-in rules.
In[5]:=
adx+bdy+cdx⋀dy%/.
%/.
| FormToOrthonormal |
| OrthonormalToForm |
Out[5]=
adx+bdy+cdx⋀dy
Out[5]=
a+b+c⋀
e
x
e
y
e
x
e
y
Out[5]=
adx+bdy+cdx⋀dy
Set spherical coordinates from the public atlas.
In[6]:=
| SetActiveSpacePreferences |
 | PublicGrassmannAtlas |
In[7]:=
{BasisType,Basis}
Out[7]=
{Vector,{,,}}
e
r
e
θ
e
φ
The transitions between bases are determined by the .
GrassmannScaleFactors
In[8]:=
GrassmannScaleFactors
Out[8]=
{1,r,rSin[θ]}
In[9]:=
a+b+c%/.
%/.
e
r
e
θ
e
φ
| VectorToOrthonormal |
| OrthonormalToVector |
Out[9]=
a+b+c
e
r
e
θ
e
φ
Out[9]=
a+br+crSin[θ]
e
r
e
θ
e
φ
Out[9]=
a+b+c
e
r
e
θ
e
φ
 |
|
 |
|
""